Arguing as in the proof of Proposition 1.2 of [1]} and using Theorems 3.6 and 3.8 of , one may show that,
for \(p,q \in (0,\infty ]\) , \(\lbrace s_{k}\rbrace  \in Y^{\alpha _{3}}_{\alpha _{1},\alpha _{2}}\)  and \(L_{\varphi } \ge [\alpha _{2}]\) , the space
\(B^{\varphi _{0}}_{p,q}(\mathbb {R}^{n},\lbrace s_{k}\rbrace )\cap S^{\prime }(\mathbb {R}^n)\)  coincides with the space \(B^{\lbrace s_{k}\rbrace }_{p,q}(\mathbb {R}^{n})\)  (Definition REF ),
the corresponding norms being equivalent.

